He says on Twitter that the truck would come after the release of a new compact SUV

Elon Musk teased details for a pickup truck that would challenge Ford Motor Co. and others in one of their most lucrative segments—though, true to form, the Tesla Inc. chief was vague about his intentions.

In comments posted Tuesday on Twitter, Mr. Musk said the truck would come after the electric-car maker releases a new compact sport-utility vehicle, which the billionaire entrepreneur has suggested could hit the road as soon as 2019.